Dark matter and galaxies: using gravitational lensing to map their relative distributions

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Abstract

Cosmological constraints from galaxy surveys are as accurate as our understanding
of the relative distributions of dark matter and galaxies, known as galaxy
bias. Weak gravitational lensing is a powerful probe of galaxy bias, since the
distortion in the shapes of distant galaxies, called shear, is directly related to the
dark matter distribution, which can be compared to the galaxy field. I look at
the galaxy clustering amplitude relative to the dark matter field, quantified by
the galaxy bias b, as well as the cross-correlation coefficient r, which tells us how
correlated the positions of galaxies are with the dark matter.
In this thesis I present several techniques to constrain galaxy bias through weak
lensing, using both numerical simulations and observational data. The most
commonly used method, using aperture statistics, is shown to be subject to
serious systematics in the presence of noisy data and scale- and time dependence
in the galaxy bias. A local comparison technique is introduced, where the
foreground distribution is used to predict the shear in the background, to which
it is compared. The technique is tested with simulations, concluding that it
requires high quality data. A model fitting approach is proposed, based on the
McDonald (2006) galaxy bias model. The two parameters of this model, a large
scale bias, b1, and a parameter, b2, that quantifies the scale dependence of the
bias, are insufficient in the presence of stochasticity. Therefore, R is introduced
as an additional parameter to take this into account.
I present galaxy bias constraints for two spectroscopic galaxy samples: the
Baryon Oscillations Spectroscopic Survey (BOSS) and the WiggleZ Dark Energy
Survey (WiggleZ), applying the traditional aperture method and the model
fitting approach to the Red Sequence Cluster Lensing Survey (RCSLenS). Both
techniques strongly suggest that galaxies trace mass, but in a complicated way,
with differences in scale- and time dependence between the samples considered.
The WiggleZ galaxy bias is found to be around b ~ 1:2, depending on redshift
and scale, and has a low cross-correlation coefficient of r ~ 0:5 at small scales.
The BOSS samples have higher bias with scale dependence around b ~ 2:0 and
show no sign of stochasticity, finding r to be close enough to unity to be explained
within a deterministic scenario. The observations are in line with previous galaxy
bias measurements from lensing data.
The thesis incorporates work on the X-ray Luminosity Function (XLF) of galaxy
clusters, measured from the Wide Angle ROSAT Pointed Survey (WARPS).
Evolution is quantified with a likelihood analysis and I conclude that it is driven
by a decreasing number density of high luminosity clusters with redshift, while the
bulk of the cluster population remains nearly unchanged out to redshift z ~ 1:1,
as expected in a low density Universe.
I conclude by investigating the impact of my galaxy bias measurements from
BOSS and WiggleZ on the growth rate of structure, as extracted from Redshift
Space Distortions (RSD). The imperfect correlation between the galaxy and
matter field, as quantified by R and b2, leads to an underestimation of the
true growth rate under the assumption of a linear bias. Therefore, in order
to constrain galaxy bias and gravity simultaneously, future cosmological redshift
surveys require high quality lensing data.